Multi-Scale Computational Framework for Smart Biomedical Implants: Thermo-Mechanical Analysis of TPMS-Based Nitinol Cranial Implants and Grain Boundary Fracture Modelling via Strain Gradient Plasticity and Cohesive Zone Methods

Abstract

The development of next-generation biomedical implants requires a rigorous understanding of material behavior across multiple length scales, from macroscale structural performance to microscale fracture physics, which govern long-term integrity. This study presents a unified multiscale computational framework that addresses both the dimensions of cranial implant applications. At the macroscale, triply periodic minimal surface (TPMS) lattice structures fabricated from Nitinol (Ni-Ti) shape memory alloy (SMA) were introduced as a meta-biomaterial architecture and numerically benchmarked against polyether ether ketone (PEEK) and Ti-6Al-4V. A fully coupled thermomechanical constitutive model based on the Zaki–Moumni formulation was implemented using FORTRAN UMAT/VUMAT subroutines interfaced with ABAQUS. At the microscale, an automated Python-based technique is presented for inserting cohesive zone elements across complex three-dimensional polycrystalline, bamboo, and columnar grain boundary topologies generated using NEPER. The bulk grain behavior is governed by a lower-order strain gradient plasticity (SGP) model that intrinsically captures the length-scale-dependent plasticity and dislocation accumulation near grain boundaries. The results were validated against experimental data and established benchmark formulations with good agreement. The macroscale results demonstrate that the TPMS-structured Nitinol achieves a Young’s modulus of approximately 5 GPa, closely matching that of the trabecular bone, while eliminating stress localization and exhibiting superior thermomechanical adaptability. At the microscale, grain boundaries are identified as the primary sites of stress concentration, and finer-grained microstructures exhibit enhanced fracture resistance. This framework provides a comprehensive numerical toolset spanning implant geometry design to grain-scale fracture, aimed at accelerating the development of mechanically optimized, smart implants.